Acts 24
24 And after some days, when Felix came with his wife Drusilla, who was Jewish, he sent for Paul and heard him concerning the faith in Christ. 25 Now as he reasoned about righteousness, self-control, and the judgment to come, Felix was afraid and answered, “Go away for now; when I have a convenient time I will call for you.” 26 Meanwhile he also hoped that money would be given him by Paul, [g]that he might release him. Therefore he sent for him more often and conversed with him.

27 But after two years Porcius Festus succeeded Felix; and Felix, wanting to do the Jews a favor, left Paul bound.

So Felix thought Paul would give him money to release him. However, Paul never gave him money. So after two years Paul was still in the captivity of the Romans and Festus took over for Felix.  Felix did not have a good track record with the Jews so that is why he left Paul bound.
So for two years he kept calling and talking to Paul. This seems kinda odd. I will do some digging on this later. If anyone has any thoughts, post them up.